K-theoretic Catalan functions

We prove that the K-k-Schur functions are part of a family inhomogenous symmetric whose top homogeneous components Catalan functions, Euler characteristics certain vector bundles on flag variety. Lam-Schilling-Shimozono identified as Schubert representatives for K-homology affine Grassmannian SLk+1. Our perspective reveals satisfy shift invariance property, and we deduce positivity their branching coefficients from result Baldwin Kumar. further show slight adjustment our formulation produces second shift-invariant basis which conjecturally has both positive rectangle factorization property. Building work Ikeda-Iwao-Maeno, conjecture this gives images Lenart-Maeno quantum Grothendieck polynomials under K-theoretic analog Peterson isomorphism.